Physics 2017 Jamb Examination

In a block and tackle system, the Velocity Ratio (V.R.) is equal to the number of pulleys in the system.
Given:
Number of pulleys (V.R.) = 6
Effort (E) = 50N
Load (L) = 200N

First, calculate the Mechanical Advantage (M.A.):\[ M.A. = \frac{\text{Load}}{\text{Effort}} = \frac{200}{50} = 4 \]
Then, calculate the efficiency (\(\eta\)):\[ \eta = \frac{M.A.}{V.R.} \times 100\% \]\[ \eta = \frac{4}{6} \times 100\% = 0.6667 \times 100\% = 66.7\% \]

For resistors connected in parallel, the reciprocal of the equivalent resistance (\(R_p\)) is the sum of the reciprocals of the individual resistances:\[ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]Given \(R_1 = R_2 = R_3 = 3\Omega\):\[ \frac{1}{R_p} = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{3}{3} = 1 \]\[ R_p = 1\Omega \]

An air conditioner is designed to stabilize the air temperature and humidity within an area. It works by removing heat and moisture from the interior of an occupied space to improve the comfort of occupants. While a refrigerator cools a small enclosed space and a compressor is a component within these systems, only the air conditioner is designed for the environmental control of a whole building.

Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons (atomic number) in each atom but different numbers of neutrons in their nuclei.

The moment of a force (or torque) is defined as the product of the force (F) and the perpendicular distance (d) from the pivot to the line of action of the force. \[ \text{Moment} = F \times d \]The S.I. unit of Force is the Newton (N) and distance is the metre (m). Therefore, the unit for the moment of a force is the Newton-metre (Nm).

In a pinhole camera, the magnification (m) relates the image height (\(h_i\)), object height (\(h_o\)), image distance (v), and object distance (u):\[ \frac{h_i}{h_o} = \frac{v}{u} \]Given:
Camera length (v) = 12cm
Object distance (u) = 60cm
Object height (\(h_o\)) = 70cm
\[ h_i = \frac{v \times h_o}{u} = \frac{12 \times 70}{60} \]\[ h_i = \frac{840}{60} = 14\text{ cm} \]

Using the heat equation \(Q = mc\Delta\theta\):
For P: \(Q = m_P c_P \Delta\theta_P\)
For Q: \(Q = m_Q c_Q \Delta\theta_Q\)
Given:
\(Q_P = Q_Q\)
\(\Delta\theta_P = 2\Delta\theta_Q\)
\(m_P = 0.5m_Q\)

Equating the heat: \[ 0.5m_Q \cdot c_P \cdot 2\Delta\theta_Q = m_Q \cdot c_Q \cdot \Delta\theta_Q \]\[ m_Q c_P \Delta\theta_Q = m_Q c_Q \Delta\theta_Q \]\[ c_P = c_Q \]The ratio \(c_P:c_Q\) is 1:1.

For a sinusoidal voltage, the peak value (\(V_0\)) is related to the root-mean-square value (\(V_{\text{rms}}\)) by:\[ V_0 = V_{\text{rms}} \times \sqrt{2} \]Given \(V_{\text{rms}} = 240\text{V}\) and \(\sqrt{2} \approx 1.414\):\[ V_0 = 240 \times 1.414 = 339.36\text{V} \]This is approximately 340V.

An AC dynamo produces current that changes direction because of the use of slip rings. To convert it to a DC dynamo, slip rings are replaced with a split-ring commutator.

The commutator reverses the connection of the coils to the external circuit every half turn, ensuring that the current flows in only one direction in the external circuit.

Assuming the diagram shows a series arrangement of two capacitors (based on common JAMB problems of this type where results are whole numbers):
For capacitors in series, the reciprocal of the total capacitance (\(C_T\)) is:\[ \frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2} \]If the capacitors are both 4.0\(\mu\)F (common values):\[ \frac{1}{C_T} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \]\[ C_T = 2.0\mu\text{F} \]Alternatively, if they are 12\(\mu\)F and 4\(\mu\)F:\[ \frac{1}{C_T} = \frac{1}{12} + \frac{1}{4} = \frac{1+3}{12} = \frac{4}{12} = \frac{1}{3} \implies 3.0\mu\text{F} \]